No, work is not considered a scalar quantity. Work is actually a scalar or a dot product of two vectors: the force applied on an object and the displacement of the object in the direction of the force. Mathematically, work (W) is defined as:
W = F ⋅ d
where F is the force vector and d is the displacement vector. The dot product of these vectors results in a scalar quantity, representing the magnitude of the work done.
The head-to-tail rule is typically used to visualize vector addition or subtraction, where vectors are represented by arrows and added or subtracted by placing the tail of one vector at the head of the other. While work involves vectors, it does not follow the head-to-tail rule because it is a scalar obtained by multiplying the magnitudes of the force and displacement vectors and the cosine of the angle between them.
In summary, work is not considered a scalar solely because it does not follow the head-to-tail rule of vectors. It is a scalar because it represents the scalar product of force and displacement vectors.